One of the difficulties with the logic here is the definitions of "guilty" and "innocent" you're using. There's actually a number of different concepts entailed within those terms, and it's rather easy to equivocate and mix things up.
The two main underlying concepts within "guilty" & "innocent" are A) did the accused in fact commit the crime and B) was the accused found culpable of the crime by the legal system. The difficulty is that while "is found legally culpable" is easy to check, " did in fact do it" is in general hard if not impossible for a third party to verify. As such, the two are often conflated, with culpability being a proxy for "did in fact do it". However, all four combinations are possible in practice.
The quadrant of "culpable & did it" is normally what one thinks of when thinking of "guilty". Also, most everyone would agree that "not culpable & didn't do it" would count as "innocent".
Where to put the two "mixed" combinations is why it's difficult to take "innocent" as a direct equivalent to "not guilty". A third party can't know for certain whether someone did in fact commit the crime, so all they have is the culpability. So it's potentially expeditious to equate "guilty" and "innocent" to "culpable" and "not culpable", respectively.
However, the conventional meaning of "innocent" is usually taken to mean more "didn't do it". So it feels like a misnomer to lump the "not culpable but did actually commit the crime" subset into the "innocent" category. As such, making "not culpable" equate to "not guilty" instead is more descriptive.
But wait, what about "didn't do it, but found culpable anyway" subset? In post-enlightenment (Western) legal systems, this is considered to be a severe miscarriage of justice, and an attempt is made to strenuously avoid it. As such, it's normally assumed that this combination rarely happens. (It's also assumed that if anyone was proven to be in this subset, their culpability status would be rapidly reassessed.) Given the difficulty of assessing commission-in-fact, if the accused is found legally culpable of the crime, it's taken that they almost certainly did in fact commit the crime. So for the small number of people who do fall into this category, you end up in a strange situation where the legal system considers them "guilty" (i.e. in the "culpable & did it" quadrant), but their advocates consider them "innocent" (in the "did not in fact commit the crime" sense, regardless of their culpability status). It's less a dispute about what to call this quadrant, and more a disagreement about whether it actually applies to any particular person.